Teaching Strategies
Polyominoes
The polyomino is remarkable well suited as a delivery mechanism for learning at this level. Being made of connected square tiles, they are easily countable for kindergarteners. This feature means the young students can readily access the advanced concepts of area and perimeter. We will sidestep the multiplicative aspects as they are not prepared for that, and they will instead be practicing counting repeatedly. As an additional bonus, square tiles are pretty much a standard supply found in primary classrooms. The children will be familiar with them. This familiarity should allow for a comfort level as the class struggles to find the tile arrangements.
Math Talks
“Learning math is not a process of acquiring a set of facts or procedures, but a process of becoming one who participates in a community that does mathematical work.”6 And in a community we share ideas, identify errors, and defend our choices. Math talk will take many forms in these lessons. Students will be working with a partner to complete tasks. During these tasks they will be discussing the shapes and attributes of their polyominoes. They can guide each other in the creation of these shapes. They can discuss the attributes and listen for inaccuracies as the counting and measuring is occurring. Students will also be talking math with me as they explain their solutions to my challenges, and defend why their choices are indeed the best choice. Another aspect of this community that does mathematical work is that through this collaboration and sharing we will be reinforcing that our classroom is a safe place for risk taking and sharing ideas.
Notice/Wonder
Notice and wonder is a regular strategy that I use in class. It appears in all content areas and is a powerful tool. Essentially it is just what it sounds like. I present an image, an equation, some words, or a physical object that the students are then asked to consider. All students are given the opportunity to share out to the class. They can choose to share an observation, make a connection, or even tell a brief story. If a student prefers he or she may ask a question about what they have examined. This strategy is excellent because every student can share out. I accept and sometimes record all responses without judgment or validation. Much like math talks, this is a great activity to maintain the ‘safe space’ atmosphere that I deeply desire in my classroom. Perhaps my favorite aspect of this strategy is that it is very open. I regularly get notices or wonders that I had never considered myself. It is unscripted and can take the class to unexpected destinations. This open aspect of the strategy also offers valuable insights into the understanding of the members of the class. It is worth keeping in mind that while observation is extremely important in mathematics, the open nature of this strategy can lead us to some challenging conversations.
Collaboration
Working together on a shared task is pretty standard fare in elementary school and my room is no exception. The benefits of collaboration are many. First, it allows kids to have a sounding board for their ideas. They can share directly to a partner, which frees me up to circulate about the classroom and listen, ask probing or guiding questions, or just take the heartbeat of the class and activity. Additionally, by regularly changing up partnerships, collaboration helps bond the students together and build trust. Trust is important to maintain that ‘safe learning place’ environment. Collaboration allows the students to step into the role of teacher for a time. I have always found that if a person can teach a thing to another then they really have an understanding of that thing. Collaboration in these activities will be crucial as two or three sets of eyes are much better at finding and interacting with the polyominoes.
Hands-On Learning
Kindergarten is the land of the manipulative. All students, but especially the young ones, learn much through a physical connection to content. Don’t look at a picture of a tree, go outside and hug one. When introducing new concepts the more concrete the better. Polyominoes are physical manipulatives that the students will be using as they are introduced to some rather abstract geometrical and measurement concepts. They will also be configuring arrangements of square tiles to find differing polyominoes. It will be invaluable to be able to work through rotations, translations, and reflections of our shapes by actually picking them up, turning them, sliding them, and flipping them. Kindergarten students are better able to understand a thing when they can make it, pick it up, manipulate it, and recreate it if necessary.
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